On CEP-Subgroups of n-Periodic Products

摘要

There is a well-known fact, that any group G_1 is a CEP-subgroup both for the direct product G_1 × G_2 and the free product G_1 * G_2 of G_1 with any group G_2. The paper gives a necessary and sufficient condition providing that a multiplier G_i of a n-periodic product Ⅱ_(iεI)~n G_i of any family of groups {G_i}_((iεI)) is a CUP-subgroup. Particularly, the found criterion means that any group G_1 of odd period n ≥ 665 is a CEP-subgroup of the n-periodic product G_1 * G_2 for any group G_2.